Exercise 24

Using your newly found understanding of cylinder and quadric surfaces, for each equation given below, write a couple sentences to describe the shape and key features of each surface. You should try to draw a good plot of each equation by hand and label your graphs.

1. $25x^2+4y^2+100z^2=100$

2. $25x^2+4y^2-100z^2=100$

3. $-25x^2-4y^2+100z^2=100$

4. $25x^2-4y^2=0$

5. $25x^2+4y^2+100z^2=0$

6. $25x^2+4y^2+100z=0$

7. $25x^2-4y^2+100z=0$

8. $-4y^2+100z=0$

9. $25x+4y+100z=100$

10. $-25x^2-4y^2-100z^2=100$

11. $25x^2-4y^2+100z^2=-100$